Question

Th half-life of ${}^{198}\text{Au}$ is 2.7 days. (a) Find the activity of a sample containing 1.00 $\mu g$ of ${}^{198}\text{Au}$. (b) What will be the activity after 7 days ? Take the atomic weight of ${}^{198}\text{Au}$ to be 198 g mo$l^{-1}$

Answer 1

(a) We know that activity = $\lambda n$

and Here $n=\frac{1\times {10}^{-6}\times 6.23\times {10}^{23}}{198}$

=$\frac{6.023\times {10}^{17}}{198}$

So, activity

$=\frac{0.963\times {10}^{17}\times 6.023}{2.7\times 198\times 24\times 3600}\times \frac{1}{3.7\times {10}^{10}}\text{Ci}$

=$0.244\text{Ci}$

(b) We know that

$\text{A}={\text{A}}_8{e}^{-\lambda r}$

=$0.244\times e^{-\frac{0.698}{8}\times 7}$

=$0.244\times e^{-1.7966}$

=$0.040\text{Ci}$